2014 Spring #1b
Hello,
Could you provide an explanation as to how we should interpret the weights with 25% written on the first day of the year? How do we average the rate in 2012? In 2015 Spring #5 I found that calculating the weights was easier to understand but in this solution I don't understand how they get those numbers. thanks!
Comments
The solution is based on this formula for current rate level factor (CRLF):
where CRL stands for Current Rate Level and ARL stands for Average Rate Level. You know CRL from part (a):
The hard part is calculating ARL. Here is my Excel spreadsheet showing the calculation with an explanation below:
We first need to know which policies are in-force on Feb 1, 2012. These would be all policies written between Feb 2, 2011 and Jan 31, 2012 so those are the only policies we have to consider. We then have to find an average rate level for all such policies.
Since we know the 25% of policies are written on Jan 1 of any year and the rest are spread uniformly throughout the rest of the year, we could have made a table with 365 rows (1 row for each day of the year) and calculated the wtd avg column for each row and summed as above but we can do it more quickly using months instead. So the way the above table works is as follows:
The last part is easier. We want a weighted average of the rate levels based on % of policies written so we multiply the second and third columns as shown and then sum. This is the ARL. Once we have that, you just compute CRL/ARL as shown.
It was a pretty hard problem.
A follow-up question on this part, am I understanding right that this question is essentially asking for the on-level premium factor for the Policy Year period from Feb 2,2011 to Feb 1,2012?
Yes, because that policy period gives rise to all the policies that would be in-force on Feb 1, 2012.